As you can see in pic we have many pics hung on walls and doors throughout the MH. Have over the years in many RV's have use Velcro strips, hangers but found that screws are the best and they will not fall out or off as other hangers will.
You have to remember the coach bounces and vibration will soon loosen the hangers and pic will fall. Your walls will have generally 1/8" plywood and about 5/8" of foam board backing that a 1" penetration will support without causing any problems with wiring that maybe in wall.
If you trade in coach later just use a white wax crayon to hide hole in wall when filled in.